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For which value of x horizontal Tangent Line

  1. Mar 30, 2008 #1
    For which value of x....horizontal Tangent Line

    1. The problem statement, all variables and given/known data

    For which value of x does f(x) = [tex]\frac{k}{ax^{2}+bx+c}[/tex] have a horizontal tangent line?


    2. Relevant equations

    Quotient Rule?

    F'(x) = [g(x)a'(x) - a(x)g'(x)]/g(x)^2?


    3. The attempt at a solution

    Am I supposed to just sub it into a quotient rule format, making the derivative equal to 0?

    So it would look like

    0 = 0 - (2ax + b)/[[ax[tex]^{2}[/tex]+bx+c][tex]^{2}[/tex]]? (and then simplify of course?)
     
    Last edited: Mar 30, 2008
  2. jcsd
  3. Mar 30, 2008 #2

    Shooting Star

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    Homework Helper

    That's correct. But there are certain restrictions on the values of a, b, and c.

    (Also, when there is only a constant in the numerator, like f(x) = k/g(x), then you can directly use f'(x) = k d/dx[1/(g(x)] = k[-g'(x)/[g(x)^2], which is nothing but the quotient rule in a lesser number of steps.)
     
  4. Mar 30, 2008 #3
    okay thanks, so the answer would just be the derivative set equal to 0?
     
  5. Mar 30, 2008 #4
    yes it is
     
  6. Mar 30, 2008 #5
    okay thanks alot
     
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